The computability and complexity of optical beam tracing

Abstract

The ray-tracing problem is considered for optical systems consisting of a set of refractive or reflective surfaces. It is assumed that the position and the tangent of the incident angle of the initial light ray are rational. The computability and complexity of the ray-tracing problems are investigated for various optical models. The results show that, depending on the optical model, ray tracing is sometimes undecidable, sometimes PSPACE-hard, and sometimes in PSPACE.<>